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Showing posts with the label Relation & Function

Domain and ranges of trigonometric functions ?

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Answer:-
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Graph of y=cosx ?

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Graph of sinx or sine function ?

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Check whether the function f:R→R,f(x)=sgn(x) is bijective or not

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Check whether the function,f: R→R ,f(x)=|x| is bijective or not

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Check whether the function ,f:R→R,f(x)=[x] is bijective or not

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Check whether the function f: (-1,1)→ R,f(x)=x/(1-x²) is bijective or not ?

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Check whether the function f:R→R ,f(x)=x³+1 is bijective or not ?

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Check whether the function f:R+→R+, f(x)=x+1/x is bijective or not

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Check whether the function f:R→R, f(x)=x² is bijective or not ?

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Check whether the function f:R→[-1,1], f(x)=sinx is bijective or not ?

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How to know a function is invertible or not ?

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If a function is both one-one & onto i.e bijective then the given function is invertible that means it has inverse. If their are two functions f & g  is said to be invertible or inverse functions, If fog=identity of x=x & gof=identity of y=y
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If f: x→y & g: y→z are bijective then prove that (gof)^-¹ =f^-¹og^-¹

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Proof:-                                                   proved
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Mind map for Relation & Function

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Prove that:If f:A→B & g:B→C both are one-one then gof:A→C is one-one.

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Proof:-                           
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Show that: a★b = a+b-ab on R–{1}, is a binary operation

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Proof:-
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Show that a~b(mod m) is an equivalence relation

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